if f(x)=4x + 3 find f^-1(x)

Answers

Answer 1

Answer:

f^-1(x) = (x-3)/4

Step-by-step explanation:

The notation f^-1(x) means that you are finding the inverse of the function f(x). To do this, you'll want to swap the "x" and the "y" in the original function, and then solve for y. Here's how:

First, we take the original function and swap the two variables:

y = 4x + 3

x = 4y + 3

Then we subtract 3 from both sides

x - 3 = 4y

Then to get y on its own, we divide both sides by 4.

y = (x-3)/4

Make sure to note that the whole expression x-3 is divided by 4, not just one part of it.

So your new inverse equation is:

f^-1(x) = (x-3)/4

Answer 2

Answer:

y = (1/4)(x - 3) is the desired inverse function of f(x) = 4x + 3.

Step-by-step explanation:

Here we're finding the 'inverse function' of the given f(x) = 4x + 3.  Follow these steps:

1.  Replace the label  f(x)  with y:  y = 4x + 3

2.  Interchange x and y:  x = 4y + 3

3.  Solve this new equation for y:  4y = x - 3, or y = (1/4)(x - 3


Related Questions

HELP IVE BEEN STUCK ON THE SAME QUESTION NOBODY WILL HELP ME I CANT CALM DOWN HELP ME

Answers

Hello! :p

[tex]\sqrt{-8}[/tex]  = [tex]2i\sqrt{2}[/tex]

[tex]\sqrt{-36}[/tex] = [tex]6i[/tex]

[tex]\sqrt{-5}[/tex] = [tex]i\sqrt{5}[/tex]

I hope you do well on your assignment! I also hope this helps! :)

A driver travels for 2 hours at 90 miles per hour, during which her car gets 30 miles per galoon of gasoline. She is paid $0.70 per mile, and her only expense is gasoline at $4 per gallon. What is her net rate of pay, in dollars per hour, after this expense?

Answers

Answer:

Her net rate of pay in dollars per hour after the expense = $26

Step-by-step explanation:

Given:

Driver travels for 2 hours.

Speed = 60 miles per hour

Her car runs at the rate of 30 miles per gallon of gasoline.

She is paid $0.50 per mile.

Expenses is price of gasoline at the rate of $2.00 per gallon.

To find her net rate of pay in dollars per hour.

Solution:

In one hour the driver travels = 60 miles

For each mile she is paid = $0.50

So, for 60 miles she will be paid =

In a gallon of gasoline the car travels = 30 miles

So, to travel 60 miles, the car would require = gallons of gasoline

1 gallon of gasoline cost = $2.00

Expenses for 2 gallons of gasoline =

So, in one hour she gets paid =$30 and her expenses for an hour drive = $4.

Thus, her net rate of pay in dollars per hour after the expense =

Brainlist please

The net rate of pay is $122 for the two hours journey.

The driver travels for 2 hours at 90 miles per hour.

Total distance travelled = 2 hours * 90 miles per hour = 180 miles

Money paid to driver = $0.70 per mile * 180 miles = $126

Fuel consumption = 30 miles per gallon, hence:

Total fuel consumption = 180 miles / (30 miles per gallon) = 6 gallon

Total expense = $4 per gallon * 6 gallon = $24

Net rate of pay = $126 - $24 = $122

The net rate of pay is $122 for the two hours journey.

Find out more on equation at: https://brainly.com/question/2972832

convert 360minutes to hour​

Answers

360 minutes is 6 hours

Answer:

6H

that was soo hard to find

A first number plus twice a second number is 5. Twice the first number plus the second totals 13. Find the numbers.

Answers

Let a and b = the numbers we must find.

a + 2b = 5.....Equation A

2a + b = 13.......Equation B

We have a system of equations in two variables.

I will solve A for little a.

a + 2b = 5

a = 5 - 2b

Now I will plug 5 - 2b for a in B.

2(5 - 2b) + b = 13

10 - 4b + b = 13

-3b = 3

b = -1

To find a, replace b with -1 in EITHER A or B.

I will use Equation A.

a + 2b = 5

a + 2(-1) = 5

a - 2 = 5

a = 7

The two numbers are -1 and 7.

Understand?

what does the term ‘slope’ mean?

Answers

Answer:

noun

1.

a surface of which one end or side is at a higher level than another; a rising or falling surface.

Step-by-step explanation:

steepness

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x)

step one: identify two points on the line

step two: select one to be (x1,y1) and the other to be (x2,y2)

step three: use the slope equation calulate slope

2x-3=8+7(+3)

2y-3(+3)=8x+7(+3)

2y=8x+10

----- --------

2y=8x+10

y=4x+5

Answer:

m=4

Pls answer me this (WILL MARK BRAINLIEST)

Answers

Answer:

a=3 b= -40

Step-by-step explanation:

.....

can someone help me find the fa tor of (128m^2n^5 - 200m^4n^3)?

Answers

Answer:

[tex]8m^2n^3[/tex], [tex]4n-5m[/tex], and [tex]4n+5m[/tex]

Step-by-step explanation:

[tex]128m^2n^5-200m^4n^3[/tex] <-- Given

[tex]m^2(128n^5-200m^2n^3)[/tex] <-- Factor out m²

[tex]m^2n^3(128n^2-200m^2)[/tex] <-- Factor out n³

[tex]8m^2n^3(16n^2-25m^2)[/tex] <-- Factor out 8

[tex]8m^2n^3(4n-5m)(4n+5m)[/tex] <-- Difference of Squares

Therefore, the factors are [tex]8m^2n^3[/tex], [tex]4n-5m[/tex], and [tex]4n+5m[/tex]

Kenny has a bag of marbles. The bag contains 8 red marbles, 5 blue marbles, and 2 yellow marbles. He will randomly select 1 marble from the bag. What is the probability Kenny will select a blue marble?

Answers

The probability Kenny would select a blue marble is 1/3.

a rectangular patio has an area of 198.4 square meters the width of the patio is 16 meters what is the length

Answers

Step-by-step explanation:

the answer thats it 12,4

Answer:

  12.4 meters

Step-by-step explanation:

The area is the product of length and width. Fill in the given information in the formula and solve for length.

  A = LW

  198.4 = L×16

  198.4/16 = L = 12.4

The length of the patio is 12.4 meters.

You rent an apartment that costs
$
1600
$1600 per month during the first year, but the rent is set to go up 11% per year. What would be the rent of the apartment during the 10th year of living in the apartment? Round to the nearest tenth (if necessary).

Answers

Answer:

$4,750

Step-by-step explanation:

Answer:

3360

Step-by-step explanation:

1600*.11*10= 1600 *.11 = 176 * 10 = 1760 + 1600 = 3360

Chromosome 13 in the human body contains a DNA molecule that is about 3.19 centimeters long.

What is the length of 1,000 of these molecules?

Answers

your answer is 3,190 centimeters. or 31.9 meters

write 0.000046 in scientific notation ​

Answers

The answer would be 4.6 x 10^-5

Hello there! :)

Numbers in scientific notation look like this:

____x10^-

The coefficient must be between 1 and 10:

4.6x10^-

Now,the exponent is how many units we move the decimal place.

The exponent for this number is negative because the number is small.

We move the decimal point 5 times to the left.

Therefore, 0.000046 in scientific notation looks like so:

4.6x10^-5

Hope it helps.

~A lonely teen who helps others with a smile

-Grace :-)

Good luck.

When testing a claim that the majority of adult Americans are against the death penalty for a person convicted of murder, a random sample of 491 adults is obtained, and 27% of them are against the death penalty (based on data from a Gallup poll). Find the P-value. Round to 4 decimals when necessary.

Answers

Using the z-distribution, it is found that the p-value is of 1.

At the null hypothesis, it is tested that the majority is not against the death penalty, that is:

[tex]H_0: p \neq 0.5[/tex]

At the alternative hypothesis, it is tested that the majority is against the death penalty, that is:

[tex]H_1: p > 0.5[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.

In this problem, the parameters are: [tex]\overline{p} = 0.27, p = 0.5, n = 491[/tex].

Then, the value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.27 - 0.5}{\sqrt{\frac{0.5(0.5)}{491}}}[/tex]

[tex]z = -10.19[/tex]

Using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is greater than a value, the p-value is of 1.

A similar problem is given at https://brainly.com/question/16313918

Plz answer I will make brainiest plzzz I need right answer ASAP!!!!!

Answers

Answer:

its 6 square feet

s = 1

1^2 = 1

6 x 1 = 6

Use traditional division to solve 6432 ÷ 24.

Answers

Ok done. Thank to me:>

Answer:

(not my answer but) its 268

Step-by-step explanation:

What is the slope of the line containing the points (-6,4) and (2,1)

Answers

In order to find the slope, we need the formula (y2-y1)/(x2-x1). The x and y represent the point (x,y). (-6,4) is our first point. (2,1) is our second point. (1-4)/2-(-)6 > -3/2+6> -3/8

The slope is -3/8.

100 Point question answered ASAP for brainliest!

Answers

Step-by-step explanation:

that is really easy too easy for that many points.

it is truly simple :

the graph (and with it the function) is shifted down by 3 units.

that means everything of the function stays the same, just the functional results are consistently lowered by 3.

so, g(x) = f(x) - 3 = -2x² - 7 - 3 = -2x² - 10

that is really all there is to it.

(2x-3)(x+5)-(x-6)(x+5)=0

Answers

X=-5,-3
That’s would be the answer
ITS POSSIBLE MAYBE I DEFINITELY DIDNT READ UR THING 7

The first term of an arithmetic sequence is 4 and the tenth term is 67.
What is the common difference? Show your work or explain your answer.

Answers

Answer:

Step-by-step explanation:

Formula

tn = a1 + (n-1)* d

Givens

tn = 67 (it is the last term or the nth term

n = 10

a1 = 4

find d

Solution

67 = 4 + (10 - 1)*d

67 = 4 + 9*d               Subtract 4 from both sides

67 - 4 = 9d            

63 = 9d                      Divide by 9

63/9 = 9d/9              

7  = d

Remark: This is a fundamental application of the arithmetic sequence. You pretty much have to know how to juggle it's parts.

The two triangle shown below are similar triangles.

What is the value of d in meters?

Answers

D is 4 metres and the scale factor is 6

pls help me asap !!!!!

Answers

Step-by-step explanation:

the option with the isoceles triangles can NOT be just of that proof, because nowhere is it defined or proven that there is or are isoceles triangles involved. even though the picture looks like it, but that does not mean anything for the formal proof.

actually, this proof is the same (and is also valid) for non-isoceles triangles.

solve pls brainliest



Marcus has picture with the dimensions of 3 ft wide and 5 ft long. He would like to change the picture using a scale factor of 1/2. What are the new dimensions for the picture and is the new picture a reduction or enlargement. Explain how you know. *

Answers

Answer:

Reduction: new dimensios are 1.5ft x 2.5ft

Step-by-step explanation:

Since he is using a scale factor of 1/2, we merely multiply everything by 1/2

3 ft * 1/2 = 1.5 ft

5 ft * 1/2 = 2.5 ft

It is obviously a reduction first since the scale factor is less than one, but you can also see that the dimensions decreased.

Answer:

The new dimensions are 1.5 ft wide and 2.5 ft long. The picture would be a reduction.

Step-by-step explanation:

Since the scale factor is less than 1 we know that the dimensions are smaller than the original. So we multiply 3 and 5 by 0.5. We get the new dimensions of 1.5ft wide by 2.5 ft long. Knowing this information we can conclude that the new picture is a reduction.

A box of 15 markers cost is $2.40 how much will a box of 40 marker’s cost

Answers

Answer:

$6.40

Step-by-step explanation:

Answer:

Step-by-step explanation:

6.4

Find the exact value of sin 29π/6
Group of answer choices

a 3/4

b 1/2

c -3/5

d 0

Answers

Answer:

b

Step-by-step explanation:

Remove full rotations of  

2

π

until the angle is between  

0

and  

2

π

.

sin

(

5

π

6

)

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

sin

(

π

6

)

The exact value of  

sin

(

π

6

)

is  

1

2

.

1

2

The result can be shown in multiple forms.

Exact Form:

1

2

Decimal Form:

0.5

The decimal form is 0.5
And it’s b. 1/2

Select all relations that represent function

Answers

Answer: All of the them except for the last relation.

Step-by-step explanation: For a relation to be a function, it can have y-values repeat but not x-values. In the last relation, you have (6,-6,), (-3,12), (6,-1), (-8,13). Notice that the x-value of 6 repeats 2 times in this relation. You can graph this relation and use the vertical line test  and you will notice that it will touch the graph more than one time. Therefore, relations 1-4 represents functions and relation 5 does not.

Hope this explanation helps.

please answer quickly!!​

Answers

Answer:

Slope: 4

Intercept: 9

Step-by-step explanation:

Hope this helped! :)

The arcs in the photo at the right appear to
be paths of stars rotating about the North Star, To produce this effect, the
photographer set a camera on a tripod and left the shutter open for an
extended time. If the photographer left the shutter open for a full 24 hours,
each are would be a complete circle. You can model a star's rotation" in the
coordinate plane. Place the North Star at the origin. Let P(1, 0) be the position
of the star at the moment the camera's shutter opens. Suppose the shutter is
left open for 2 h 40 min, with the arc ending at P. a. What angle of rotation
maps Ponto P? b. What are the x and y coordinates of P to the nearest
thousandth? c. What translation rule maps P onto P?

Answers

Answer:

a. What angle of rotation maps Ponto P?

30.25 degrees

b. What are the x and y coordinates of P to the nearest thousandth?

(83.3, 33.3)

c. What translation rule maps P onto P?

Rotation

please help me Im lost on this :(​

Answers

Answer:

C

Step-by-step explanation:

the quadratic formula is

[tex] \frac{ - b + \sqrt{b ^{2} - 4ac} }{2a} [/tex]

Make the quadratic equal to 0, so it will be 3x^2 + 8x -2=0. Then substitute the values into the equation.

Answer: C) 3x^2+8x-10=-8

Step-by-step explanation:

3x^2+8x-10x=-8

3x^2+8x-2=0

a=3 b=8 c=-2

Plug it into quadratic formula.

Use the graph of △ABC with midsegments DE, EF and DF. Show that EF is parallel to AC and that EF=1/2 AC

Answers

According to the midsegment theorem, the midsegments are parallel to

and half the length of the opposite side.

The completed statement are as follows;

Because the slopes of [tex]\overline{EF}[/tex] and [tex]\overline{AC}[/tex] are both -4, [tex]\overline{EF}[/tex] ║ [tex]\overline{AC}[/tex]EF = [tex]\underline{\sqrt{17}}[/tex] and AC = [tex]\underline{2 \cdot \sqrt{17} }[/tex]Because [tex]\underline{\sqrt{17} }[/tex] = [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17} }[/tex], [tex]EF = \frac{1}{2} \cdot AC[/tex]

Reasons:

From the given graph of ΔABC, we have;

Coordinates of the points A, B, and C are; A(-5, 2), B(1, -2), and C(-3, -6)

The coordinates of the point D and E on [tex]\mathbf{\overline{DE}}[/tex] are; D(-4, -2), and E(-2, 0)

The coordinates of the point F is; F(-1, -4)

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]\displaystyle Slope \ of \ line \ \overline{AC} = \mathbf{\frac{(-6) - 2}{-3 - (-5)} = \frac{-8}{2}} = -4[/tex]

[tex]\displaystyle Slope \ of \ line \ \overline{EF} = \frac{0 - (-4)}{-2 - (-1)} = \frac{4}{-1} = -4[/tex]

[tex]Length \ of \ segment,\ l = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]

Length of EF  = √((-1 - (-2))² + (-4 - 0)²) = √(17)

Length of AC = √((-3 - (-5))² + (-6 - 2)²) = √(4 × 17) = 2·√(17)

Therefore, we have;

Because the slope of [tex]\mathbf{\overline {EF}}[/tex] and [tex]\mathbf{\overline {AC}}[/tex] are both , -4, [tex]\overline {EF}[/tex] ║ [tex]\overline {AC}[/tex]. EF = [tex]\underline{\sqrt{17}}[/tex], and AC

= [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}[/tex],. Because [tex]\underline{\sqrt{17}}[/tex] = [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}[/tex], [tex]EF =\mathbf{ \frac{1}{2} AC}[/tex]

Learn more about midsegment theorem of a triangle here:

https://brainly.com/question/7423948

The terminal side of an angle θ in standard position passes through the point (3, 1). Calculate the exact values of the six trig functions for angle θ.

Answers

Answer:

sin α = [tex]\frac{y}{r}[/tex] = [tex]\frac{1}{\sqrt{10} }[/tex]

cos α = [tex]\frac{x}{r}[/tex] = [tex]\frac{3}{\sqrt{10} }[/tex]

tan α = [tex]\frac{y}{x}[/tex] = [tex]\frac{1}{3}[/tex]

cot α = [tex]\frac{x}{y}[/tex] = [tex]\frac{3}{1}[/tex]

sec α = [tex]\frac{r}{x}[/tex] = [tex]\frac{\sqrt{10} }{3}[/tex]

csc α = [tex]\frac{r}{y}[/tex] = [tex]\frac{\sqrt{10} }{1}[/tex]

Step-by-step explanation:

If the point is given on the terminal side of an angle, then:

Calculate the distance between the point given and the origin:

r = [tex]\sqrt{x^2+y^2}[/tex]

Here it is: [tex]\sqrt{3^2+1^2}[/tex] = [tex]\sqrt{9+1}[/tex] = [tex]\sqrt{10}[/tex]

So we have:

x = 3

y = 1

r = [tex]\sqrt{10}[/tex]

Now we can calculate all 6 trig, functions:

sin α = [tex]\frac{y}{r}[/tex] = [tex]\frac{1}{\sqrt{10} }[/tex]

cos α = [tex]\frac{x}{r}[/tex] = [tex]\frac{3}{\sqrt{10} }[/tex]

tan α = [tex]\frac{y}{x}[/tex] = [tex]\frac{1}{3}[/tex]

cot α = [tex]\frac{x}{y}[/tex] = [tex]\frac{3}{1}[/tex]

sec α = [tex]\frac{r}{x}[/tex] = [tex]\frac{\sqrt{10} }{3}[/tex]

csc α = [tex]\frac{r}{y}[/tex] = [tex]\frac{\sqrt{10} }{1}[/tex]

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